CN112415045B - A device and method for measuring thermal adaptation coefficient of materials under low air pressure - Google Patents
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Abstract
The invention discloses a device and a method for measuring a material thermal adaptability coefficient at low air pressure. The device comprises two chambers with the same structure and different inner diameters, wherein each chamber comprises a conductive filament, a top cover, a chamber wall and a bottom cover; a pipeline is arranged on the top cover; the chamber wall is radially provided with a first supporting rod, a second supporting rod, a third supporting rod and a fourth supporting rod which extend to the center of the chamber; the end of the supporting rod is provided with a lantern ring; the conductive filaments penetrate through the four lantern rings; the first support rod and the fourth support rod are provided with conducting wires; the outer part of the lead penetrates out of the wall of the chamber to be connected to a direct current power supply, and one end of the inner part of the lead is connected to the conductive filament; the second support rod and the third support rod are provided with conducting wires; one end of the wire is connected to a voltmeter at the outer part, and one end of the wire is connected to the conductive filament at the inner part; the wall of the chamber is provided with a pressure gauge; the temperature measuring element, the pressure gauge and the voltmeter are all connected to the computer. The device is utilized to collect relevant data at low pressure, a data curve is fitted, and the thermal adaptability coefficient is obtained through calculation. The method has high measurement precision and good reliability.
Description
Technical Field
The invention belongs to the technical field of thermodynamic parameter measurement, and particularly relates to a device and a method for measuring a thermal adaptation coefficient between gas and solid.
Background
The thermal adaptation coefficient is a physical parameter representing the degree of energy exchange between a solid and gas, namely the complete degree of energy exchange when gas molecules collide with a solid wall surface, and has a wide application prospect in engineering application. In the field of aerospace, if the service life of a spacecraft in space needs to be accurately calculated, the thermal adaptation coefficient of gas molecules needs to be used; the coefficient of thermal accommodation is also important in cases involving heat transfer between gas and solid. Therefore, the accurate acquisition of the thermal adaptation coefficient has important significance for heat exchange analysis and the like in engineering application.
At this stage, the technique for measuring the thermal adaptation coefficient is still relatively lacking, and is generally obtained by experiments or by consulting the literature. Therefore, the empirical thermal adaptive coefficient is often lack of real accuracy, because the thermal adaptive coefficient is related to many factors, including the type of gas, the state of the solid surface, whether molecules of other gases are adsorbed on the solid surface, and the temperature difference between the gas and the wall surface of the solid. A method and apparatus are therefore presented herein that can actually measure the coefficient of thermal adaptation.
Patent No. CN108241303A utilizes a calculation method of vacuum plume effect to fit the thermal adaptive coefficient of the wall surface according to the monte carlo principle. The method can calculate the thermal adaptive coefficient of the wall surface through numerical simulation, but the molecular dynamics theory has the problems of large calculated amount and small calculated domain, and can not be directly applied to the condition that the analysis domain is large, such as the condition that the analysis domain can not be directly applied to a spacecraft, so as to obtain the thermal adaptive coefficient of the surface of the spacecraft; meanwhile, the fitting result may have a large difference with the rail test result, and multiple feedback corrections are required. The experimental method mentioned herein is not limited to the size of the model, and the thermal adaptive coefficient of the gas and the wall surface can be directly calculated according to the experimental data.
Patent CN102799074A discloses a lithographic apparatus and components, and discusses the application of thermal adaptive coefficients in lithography. The efficiency and quality of the lithography technology at different thermal adaptation coefficients are compared, the concept of the effective thermal adaptation coefficient is introduced, and the lithography technology has better processing efficiency and quality when the effective thermal adaptation coefficient is higher. Therefore, the thermal adaptation coefficient also plays an important role in the application of the lithography technology, but a specific method for calculating the thermal adaptation coefficient of the material is not mentioned in the text, so a theoretical method and a measuring device capable of calculating the thermal adaptation coefficient of the material are provided in the text.
Disclosure of Invention
The invention provides a device and a method for measuring the thermal adaptive coefficient of a material, aiming at the problems in the prior art. The device provided by the invention is simple in structure and convenient to build; the provided method has the advantages of simple principle, convenient operation and accurate measurement result.
An apparatus for measuring the thermal adaptability coefficient of a material at low pressure,
comprises two chambers with the same structure and different inner diameters,
the chamber comprises a conductive filament (5), a top cover (14), a chamber wall (12) and a bottom cover (15) forming a sealing structure;
a pipeline (16) is arranged on the top cover (14);
the chamber wall (12) is radially provided with a first supporting rod, a second supporting rod, a third supporting rod and a fourth supporting rod which extend to the center of the chamber; the end of the supporting rod is provided with a lantern ring; the conductive filaments (5) penetrate through the four lantern rings;
the first support rod and the fourth support rod are provided with conducting wires; the outer part of the lead passes through the chamber wall (12) and is connected to a direct current power supply (11), and one end of the inner part of the lead is connected to the conductive filament (5);
the second support rod and the third support rod are provided with conducting wires; the external end of the lead is connected to a voltmeter (10), and the internal end of the lead is connected to the conductive filament (5);
a temperature measuring element is arranged in the cavity;
the chamber wall (12) is provided with a pressure gauge (9) for measuring the chamber pressure.
The temperature measuring element, the pressure gauge (9) and the voltmeter (10) are all connected to the computer (18).
The low-pressure measurement environment of the invention refers to that gas in a chamber is in a free molecular region under low pressure, and at the moment, gas molecules only collide with a solid wall surface to exchange energy.
Further, the diameter of the conductive filaments (5) is less than 100 μm. The diameter of the filaments is small enough to ensure that no temperature gradients occur in the radial direction.
Furthermore, sealing rings (13) are arranged between the top cover (14), the bottom cover (15) and the chamber wall (12).
Furthermore, a first temperature measuring element and a second temperature measuring element are arranged in the cavity, the first temperature measuring element (6) is arranged on the conductive filament (5), and the second temperature measuring element (7) is suspended in the cavity and is respectively used for measuring the temperature of the conductive filament and the temperature in the cavity.
Further, the inner diameters of the lantern rings are the same, and the inner walls of the lantern rings are coated with insulating coatings.
Furthermore, the surface of the support rod is sprayed with an insulating coating, and only the conductive filaments (5) are conducted with the conducting wires.
Further, the pipe (16) is provided with a valve (17).
Further, the computer is used for collecting temperature, pressure and voltage values.
Another object of the present invention is to provide a method for measuring the thermal adaptation coefficient of a material under a low air pressure by using the above apparatus, comprising the steps of:
(1) according to the rarefied gas dynamics, when the Kn is more than or equal to 10, the Knudsen is in the free molecular flow field, which means that molecules rarely collide with each other in a region with a relatively large range near an object, the gas molecules can be considered to collide and exchange energy with a solid wall surface only, and the characteristic point pressure P reaching a free molecular region (Kn is made to be 10) is calculated according to the following formula0:
In the formula, Kn is the Knudsen number, P is the gas pressure, lambda is the mean molecular free path, and kBIs the Boltzmann constant, D1The diameter of the filament, d the diameter of the gas molecule, the effective diameter of the air is generally 0.35 nm, and when the filament is heated to a small temperature (generally below 30 ℃), T ism,DFTo calculate the effective average temperature at Kn, which is the average of the filament temperature and the ambient temperature, T can be determined from the filament temperature and the ambient temperaturem,DFLet Kn be 10 to find the characteristic point pressure P of gas reaching the free molecular region0；
(2) According to the calculated P0The chamber is pumped to vacuum by a pump, so that the air pressure in the chamber reaches P0Hereinafter, the air pressure value at this time is denoted as P1；
(3) Passing a step current to the conductive filament using a DC power supply and recording the initial value of the voltage U between the electrode nodes at step times 2 and 30After the electric heating reaches the steady state, measuring the voltage stable value U between the 2 and 3 electrode nodes1；
(4) According to U0And U1And other known parameters, the natural convective heat transfer coefficient h can be calculated using the following equation:
in the formula, h is the measured natural convection heat transfer coefficient, U1Recording the steady state value of the voltage after reaching the new steady state for the voltmeter, U0Obtaining a voltage initial value corresponding to the step time of the step current for the voltmeter, wherein delta is the resistance temperature coefficient of the conductive filament material, Q is the Joule heating power of the filament after the filament is electrified to reach a new steady state by the step current peak value, L is the length of the filament, S is the perimeter of the cross section of the filament, A is the area of the cross section of the filament, and k is the area of the cross section of the filamentwireIs the thermal conductivity of the filament material. In order to avoid the influence of electrode resistance heat generation on the measured value, the voltage on the filament is measured by a voltmeter between the nodes of the 2 and 3 electrodes, the current does not pass through the 2 and 3 electrodes, the introduction of the electrode resistance can be avoided, the influence caused by the electrode heat generation is eliminated, and the convection heat transfer coefficient h in the current cavity and under the current air pressure is calculated;
(5) according to the following formula:
in the formula, D1Is the diameter of the filament, D2Is the inner diameter of the cylindrical chamber, gamma is the specific heat ratio of the gas, and the specific heat ratio of the air is 1.40 and T is related to the type of the gasm,DFTo calculate the effective average temperature, T, at Knm,FMFor the effective average temperature of the gas in the free molecular regime, T is the temperature at which the filament temperature is close to the ambient temperature in the chamber (the filament temperature rise is sufficiently small, typically below 30 degrees), Tm,DF≈Tm,FMI.e. by
Nu in the formulafreePositively correlated with 1/KnAnd the correlation coefficient is only related to two thermal adaptation coefficients alpha1、α2In connection with, alpha1Is the coefficient of thermal adaptation between gas and filament, alpha2The thermal adaptation coefficient between the gas and the inner wall surface of the chamber;
(6) according to the convective heat transfer coefficient h obtained by calculation, the Nu of the free molecular region is calculated by using the following formulafree：
In the formula, h is the convective heat transfer coefficient in the current cavity and at the current air pressure, and D1Is the diameter of the filament, kgasCalculating Knudsen number and gas pressure P according to h as heat conductivity coefficient of gas1The Nu number of Nufree,1；
(7) The reciprocal number 1/Kn of the knudsen number at the current air pressure is obtained according to the following formula:
in the formula, kBIs the Boltzmann constant, D1The diameter of the filament, d the diameter of the gas molecule, the effective diameter of the air is generally 0.35 nm, and when the temperature of the filament rises very little (the temperature of the filament rises below 30 ℃), T ism,DFThe average of the filament temperature and the ambient temperature, the gas pressure P1The result of the calculation is recorded as 1/Kn1；
(8) Changing the air pressure in the chamber for a plurality of times, repeating the steps (2) to (7) and keeping the air pressure P1～PnObtain multiple sets of data (Nu)free,1，1/Kn1)～(Nufree,n，1/Knn)；
(9) Fixing the same filament material in another chamber with different inner diameter, repeating all the above steps to obtain different D2The other group of (Nu)free1/Kn) } data;
(10) using { (Nu) according to the following equation free1/Kn) } dataCan draw the Nu of Nu's NufreeLine of relationship for the reciprocal number 1/Kn of knudsen:
from the formula, when the inner diameter D of the chamber2Value is respectively taken as D2 narrowAnd D2 widthTime, NufreeThe correlation coefficient with 1/Kn will also be different, so two sets of data obtained experimentally in chambers of different internal diameters { (Nu)free, narrow，1/KnNarrow and narrow) And { (Nu)free, wide，1/KnWidth of) Can draw two relation lines with different slopes, and the slopes of the two relation lines are respectively recorded as kNarrow and narrowAnd kWidth ofBecause the temperature rise of the filament is small enough (the temperature rise of the filament is below 30 ℃),
then the slope kNarrow and narrowAnd kWidth ofWritten as follows:
solving equation solution alpha1And alpha2：
The heat exchange coefficient alpha between the gas and the filament surface is obtained1And the heat transfer coefficient alpha between the gas and the inner wall surface of the chamber2。
Under different air pressure conditions, the invention can calculate the corresponding convective heat transfer coefficient h and further calculate the Nu of the NufreeAnd the reciprocal knudsen number of 1/Kn.
According to the equation:
nufreeIs positively correlated with the reciprocal 1/Kn of the Kenusen number, and has a proportionality coefficient and two thermal adaptation coefficients alpha1、α2In connection with this, experiments were carried out with electrically conductive filaments placed in two chambers of different internal diameters, obtaining two different sets of data { (Nu)free, narrow，1/KnNarrow and narrow) And { (Nu)free, wide，1/KnWidth of) Drawing two relation lines with different slopes, and solving alpha according to the slope simultaneous equation of the two lines1And alpha2So as to obtain a thermal adaptation coefficient alpha between the gas and the filament material1And a coefficient of thermal adaptation alpha between the gas and the inner wall surface of the chamber2。
The invention has the beneficial effects that:
the invention provides a method and a device for simply and quickly measuring the thermal adaptation coefficient between gas and a material. The device can replace conductive filaments and chamber walls made of different materials, fill different types of gases, and regulate and control the air pressure in the chamber, so that the energy exchange between gas molecules and the materials under different conditions is researched, specific experimental conditions are related to the size and other parameters of the materials, the flexibility and the variability are realized, the device is simple, the measurement precision is high, the reliability is good, the measurement application range is wide, and the effective measurement for obtaining the thermal adaptation coefficient between the gas and the materials is realized.
The testing device provided by the invention is simple in structure and convenient to build; the provided measuring method is convenient to operate and accurate in measuring result.
Drawings
FIG. 1 is a schematic structural diagram of an apparatus for measuring the thermal adaptive coefficient of a material under low pressure;
reference numerals: 1-a first supporting rod, 2-a second supporting rod, 3-a third supporting rod, 4-a fourth supporting rod, 5-a conductive filament, 6-a first temperature measuring element, 7-a second temperature measuring element, 8-a conducting wire, 9-a pressure gauge, 10-a voltmeter, 11-a DC power supply, 12-a chamber wall, 13-a sealing ring, 14-a top cover, 15-a bottom cover, 16-a pipeline, 17-a valve and 18-a computer;
FIG. 2 is two chambers of different inside diameters;
FIG. 3 is a graph of h as a function of air pressure;
FIG. 4 shows NufreeGraph relating to the reciprocal 1/Kn of the knudsen number.
Detailed Description
The present invention will be further described with reference to specific examples, which are not intended to limit the scope of the present invention.
Examples
Fig. 1 shows an apparatus for measuring the thermal adaptability coefficient of a material under low pressure, which comprises two chambers with the same structure and different inner diameters,
the chamber comprises a conductive filament 5, a top cover 14, a chamber wall 12 and a bottom cover 15, and a sealing structure is formed among the top cover 14, the bottom cover 15 and the chamber wall 12 by arranging a sealing ring 13;
the top cover 14 is provided with a pipeline 15, and the pipeline 15 is provided with a valve 16. The conduit 16 is for connection to a vacuum pump.
The chamber wall 12 is radially provided with first to fourth support rods which extend to the center of the chamber; the end of the supporting rod is provided with a lantern ring; the conductive filament 5 penetrates through the four lantern rings; the diameter of the conductive filaments 5 is less than 100 μm, the diameter of the filaments being sufficiently small to ensure that no temperature gradient occurs in the radial direction; the inner diameters of the lantern rings are the same, and the inner walls of the lantern rings are coated with insulating patterns;
the first supporting rod 1 and the fourth supporting rod 4 are provided with conducting wires; the outside of the lead passes through the chamber wall 12 and is connected to a direct current power supply 11, and one end of the inside of the lead is connected to the conductive filament 5;
the second supporting rod 2 and the third supporting rod 3 are provided with conducting wires; the wire has an outer end connected to a voltmeter 10 and an inner end connected to the conductive filament 5;
the surface of the support rod is sprayed with an insulating coating, and only the conductive filaments 5 are conducted with the wires 8;
a first temperature measuring element and a second temperature measuring element are arranged in the cavity, the first temperature measuring element 6 is arranged on the conductive filament 5, and the second temperature measuring element 7 is hung in the cavity and is respectively used for measuring the temperature of the conductive filament 5 and the temperature in the cavity;
the chamber wall 12 is provided with a pressure gauge 9 for measuring the chamber pressure;
the temperature measuring element, the pressure gauge 9 and the voltmeter 10 are all connected to the computer 18 to collect temperature, pressure and voltage values.
The low-pressure measurement environment of the invention refers to that gas in a chamber is in a free molecular region under low pressure, and at the moment, gas molecules only collide with a solid wall surface to exchange energy.
The method for measuring the thermal adaptive coefficient of the material under low air pressure by using the device comprises the following steps:
(1) according to the rarefied gas dynamics, when the Kn is more than or equal to 10, the Knudsen is in the free molecular flow field, which means that molecules rarely collide with each other in a region with a rather large range near an object, the gas molecules can be considered to collide with a solid wall surface and exchange energy, namely the gas molecules in the chamber can be considered to collide between the filaments 5 and the inner wall surface, and the characteristic point pressure P reaching the free molecular zone (Kn is 10) is calculated according to the following formula0:
In the formula, Kn is the Knudsen number, P is the gas pressure, lambda is the mean molecular free path, and kBIs the Boltzmann constant, D1The diameter of the filament, d the diameter of the gas molecule, the effective diameter of the air is generally 0.35 nm, and when the filament is heated to a small temperature (generally below 30 ℃), T ism,DFTo calculate the effective average temperature at Kn, which is the average of the filament temperature and the ambient temperature, the filament temperature and the ambient temperature are measured by the temperature measuring element 6 and the temperature measuring element 7, respectively, and T is determinedm,DFLet us orderCalculating the characteristic point pressure P of gas reaching the free molecular zone by Kn-100；
(2) According to the calculated characteristic point pressure P0The chamber is pumped to vacuum by a pump, so that the air pressure in the chamber reaches P0Hereinafter, in the free molecular region, the air pressure value at this time is denoted as P1；
(3) Passing a step current to the conductive filament using a DC power supply and recording the initial value of the voltage U between the electrode nodes at step times 2 and 30After the electric heating reaches the steady state, measuring the voltage stable value U between the 2 and 3 electrode nodes1；
(4) According to U0And U1And other known parameters, the natural convective heat transfer coefficient h can be calculated using the following equation:
in the formula, h is the measured natural convection heat transfer coefficient, U1Recording the steady state value of the voltage after reaching the new steady state for the voltmeter, U0Obtaining a voltage initial value corresponding to the step time of the step current for the voltmeter, wherein delta is the resistance temperature coefficient of the conductive filament material, Q is the Joule heating power of the filament after the filament is electrified to reach a new steady state by the step current peak value, L is the length of the filament, S is the perimeter of the cross section of the filament, A is the area of the cross section of the filament, and k is the area of the cross section of the filamentwireIs the thermal conductivity of the filament material. In order to avoid the influence of electrode resistance heat generation on the measured value, the voltage on the filament is measured by a voltmeter between the nodes of the 2 and 3 electrodes, the current does not pass through the 2 and 3 electrodes, the introduction of the electrode resistance can be avoided, the influence caused by the electrode heat generation is eliminated, and the convection heat transfer coefficient h in the current cavity and under the current air pressure is calculated;
(5) according to the following formula:
in the formula, D1Being filamentsDiameter, D2Is the inner diameter of the cylindrical chamber, gamma is the specific heat ratio of the gas, and the specific heat ratio of the air is 1.40 and T is related to the type of the gasm,DFTo calculate the effective average temperature, T, at Knm,FMFor the effective average temperature of the gas in the free molecular regime, T is measured when the filament temperature is close to the ambient temperature in the chamber (the filament temperature rise is small, typically below 30 degrees)m,DF≈Tm,FMI.e. by
Nu in the formulafreeIs positively correlated with 1/Kn, and the correlation coefficient is only related with two thermal adaptation coefficients alpha1、α2In connection with, alpha1Is the coefficient of thermal adaptation, alpha, between the gas and the filaments 52The thermal adaptation coefficient between the gas and the inner wall surface of the chamber;
(6) according to the convective heat transfer coefficient h obtained by calculation, the Nu of the free molecular region is calculated by using the following formulafree：
In the formula, h is the convective heat transfer coefficient in the current cavity and at the current air pressure, and D1Is the diameter of the filament, kgasCalculating Knudsen number and gas pressure P according to h as heat conductivity coefficient of gas1The Nu number of Nufree,1；
(7) The reciprocal number 1/Kn of the knudsen number at the current air pressure is obtained according to the following formula:
in the formula, kBIs the Boltzmann constant, D1The diameter of the filament, d the diameter of the gas molecule, the effective diameter of the air is generally 0.35 nm, and when the temperature of the filament rises very little (the temperature of the filament rises below 30 ℃), T ism,DFThe average of the filament temperature and the ambient temperature, the gas pressure P1The result of the calculation is recorded as1/Kn1；
(8) Changing the air pressure in the chamber for a plurality of times, repeating the steps (2) to (7) and keeping the air pressure P1～PnThe lower convective heat transfer coefficient h changes, the change of h with the air pressure is shown in FIG. 3, different h correspond to different Nu' sfreeFinally, a plurality of groups of data (Nu) are obtainedfree,1，1/Kn1)～(Nufree,n，1/Knn)；
(9) Fixing the same filament material in another chamber with different inner diameter, repeating all the above steps to obtain different D2The other group of (Nu)free1/Kn) } data;
(10) using { (Nu) according to the following equation free1/Kn) } data can be plotted against the NufreeThe line of the relationship for the reciprocal number 1/Kn of knudsen is shown in fig. 4:
from the formula, when the inner diameter D of the chamber2At different times NufreeThe correlation coefficient with 1/Kn is also different, so that the inner diameter is D2 narrowAnd D2 widthTwo sets of data { (Nu) were obtained from two laboratory experimentsfree, narrow，1/KnNarrow and narrow) And { (Nu)free, wide，1/KnWidth of) Obtaining two relation lines with different slopes from the obtained data, and recording the slopes of the two relation lines as kNarrow and narrowAnd kWidth ofBecause the temperature rise of the filament is small enough (the temperature rise of the filament is below 30 ℃),
then the slope kNarrow and narrowAnd kWidth ofWritten as follows:
solving equation solution alpha1And alpha2：
The heat exchange coefficient alpha between the gas and the filament surface is obtained1And the heat transfer coefficient alpha between the gas and the inner wall surface of the chamber2。
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any modification, equivalent replacement, and improvement made by those skilled in the art within the technical scope of the present invention should be included in the scope of the present invention.
Claims (9)
1. An apparatus for measuring the coefficient of thermal adaptability of a material at low air pressure, comprising:
comprises two chambers with the same structure and different inner diameters,
the chamber comprises a conductive filament (5), a top cover (14), a chamber wall (12) and a bottom cover (15) forming a sealing structure; two temperature measuring elements are arranged in the cavity;
a pipeline (16) is arranged on the top cover (14);
the chamber wall (12) is radially provided with a first supporting rod, a second supporting rod, a third supporting rod and a fourth supporting rod which extend to the center of the chamber; the end of the supporting rod is provided with a lantern ring; the conductive filaments (5) penetrate through the four lantern rings;
the first support rod and the fourth support rod are provided with conducting wires; the outer part of the lead passes through the chamber wall (12) and is connected to a direct current power supply (11), and one end of the inner part of the lead is connected to the conductive filament (5);
the second support rod and the third support rod are provided with conducting wires; the external end of the lead is connected to a voltmeter (10), and the internal end of the lead is connected to the conductive filament (5);
the chamber wall (12) is provided with a pressure gauge (9);
the temperature measuring element, the pressure gauge (9) and the voltmeter (10) are all connected to the computer (18).
2. The apparatus of claim 1, wherein: the diameter of the conductive filaments (5) is less than 100 μm.
3. The apparatus of claim 1, wherein: sealing rings (13) are arranged between the top cover (14), the bottom cover (15) and the chamber wall (12).
4. The apparatus of claim 1, wherein: one of the two temperature measuring elements is arranged on the conductive filament (5), and the other temperature measuring element is suspended in the cavity.
5. The apparatus of claim 1, wherein: the inner diameters of the lantern rings are the same, and the inner walls of the lantern rings are coated with insulating coatings.
6. The apparatus of claim 1, wherein: the surface of the support rod is sprayed with an insulating coating, and only the conductive filaments (5) are conducted with the conducting wires.
7. The apparatus of claim 1, wherein: the pipeline (16) is provided with a valve (17).
8. The apparatus of claim 1, wherein: the computer is used for collecting temperature, pressure and voltage values.
9. A method for measuring the coefficient of thermal accommodation of a material at low atmospheric pressure using the apparatus of any one of claims 1 to 8, comprising the steps of:
(1) calculating the characteristic point pressure P reaching the free molecular region according to the rarefied gas dynamics formula0：
In the formula, Kn is the Knudsen number, P is the gas pressure, lambda is the mean molecular free path, and kBIs the Boltzmann constant, D1Is the diameter of the filament, d is the diameter of the gas molecule, Tm，DFTo calculate the effective average temperature at Kn, which is the average of the temperature of the conductive filament and the ambient temperature, the characteristic point pressure P at which the gas reaches the free molecular regime is determined by taking Kn 100；
(2) According to the calculated characteristic point pressure P0The chamber is pumped to vacuum by a pump, so that the air pressure in the chamber reaches P0Hereinafter, in the free molecular region, the air pressure value at this time is denoted as P1；
(3) Passing a step current to the conductive filament using a DC power supply and recording the initial value U of the voltmeter at the step time0After the electric heating reaches the steady state, measuring the stable value U of the voltmeter1；
(4) According to U0And U1And other known parameters, the natural convective heat transfer coefficient h can be calculated using the following equation:
in the formula, h is the measured natural convection heat transfer coefficient, U1Recording the steady state value of the voltage after reaching the new steady state for the voltmeter, U0Obtaining a voltage initial value corresponding to the step time of the step current for the voltmeter, wherein delta is the resistance temperature coefficient of the conductive filament material, Q is the Joule heating power of the filament after the filament is electrified to reach a new steady state by the step current peak value, L is the length of the filament, S is the perimeter of the cross section of the filament, A is the area of the cross section of the filament, and k is the area of the cross section of the filamentwireIs the thermal conductivity of the filament material;
calculating the convective heat transfer coefficient h in the current cavity and under the current air pressure;
(5) according to the following formula:
in the formula, D1Is the diameter of the filament, D2Is the inner diameter of the cylindrical chamber, gamma is the specific heat ratio of the gas, the specific heat ratio of the air is generally 1.40, Tm，DFTo calculate the effective average temperature, T, at Knm，FMIs the effective average temperature of the gas in the free molecular region;
when the filament temperature is close to the ambient temperature in the chamber, Tm，DF≈Tm，FMI.e. by
Nu in the formulafreeIs positively correlated with 1/Kn, and the correlation coefficient is only related with two thermal adaptation coefficients alpha1、α2In connection with, alpha1Is the coefficient of thermal adaptation, alpha, between the gas and the conductive filaments 52The thermal adaptation coefficient between the gas and the inner wall surface of the chamber;
(6) according to the convective heat transfer coefficient h obtained by calculation, the Nu of the free molecular region is calculated by using the following formulafree：
In the formula, h is the convective heat transfer coefficient in the current cavity and at the current air pressure, and D1Is the diameter of the filament, kgasIs the thermal conductivity of the gas;
calculating the Knudel number and the air pressure P according to h1The Nu number of Nufree，1
(7) The reciprocal number 1/Kn of the knudsen number at the current air pressure is obtained according to the following formula:
in the formula, kBIs the Boltzmann constant, D1Is the diameter of the filament, d is the diameter of the gas molecule, the effective diameter of the air is generally 0.35 nm, and when the filament temperature rises very little, T ism，DFThe average of the filament temperature and the ambient temperature, the gas pressure P1The result of the calculation is recorded as 1/Kn1；
(8) Changing the air pressure in the chamber for a plurality of times, repeating the steps (2) to (7) and keeping the air pressure P1～PnThe lower convection heat transfer coefficient h changes, and different h correspond to different NufreeFinally, a plurality of groups of data (Nu) are obtainedfree，1，1/Kn1)～(Nufree，n，1/Knn)；
(9) Fixing the same filament material in another chamber with different inner diameter, repeating all the above steps to obtain different D2The other group of (Nu)free1/Kn) } data;
(10) using { (Nu) according to the following equationfree1/Kn) } data can be plotted against the NufreeLine of relationship for the reciprocal number 1/Kn of knudsen:
inner diameter of D2 narrowAnd D2 widthTwo sets of data { (Nu) were obtained from two laboratory experimentsfree, narrow，1/KnNarrow and narrow) And { (Nu)free, wide，1/KnWidth of) And obtaining two relation lines with different slopes, and recording the slopes of the two relation lines as kNarrow and narrowAnd kWidth ofSince the temperature rise of the filament is small enough,
then the slope kNarrow and narrowAnd kWidth ofWritten as follows:
solving equation solution alpha1And alpha2：
The heat exchange coefficient alpha between the gas and the filament surface is obtained1And the heat transfer coefficient alpha between the gas and the inner wall surface of the chamber2。
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